Conclusion

This chapter reconnects the results presented to the problems illustrated in the Introduction.

Elements of Experimental Computing

This Chapter starts by considering the third foundation: computing as an experimental science. It overviews the origin of the term, the early positions on experimental computer science and introduces two basic notions of computational hypothesis and computational experiment essential to the understanding of computing as an experimental discipline.

Specification and Implementation

This chapter considers the need to understand the relation between specification and implementation of computing systems, and to clarify the problem of miscomputation.

The First Generation of Computers

This chapter starts with the analysis of the engineering foundation of computing which, proceeding in parallelwith themathematical foundation, led to the design and creation of physical computingmachines. It illustrates the historical evolution of the first generation of computing and their technical foundation, known as the von Neumann architecture. Fromthe conceptual point of view, the chapter clarifies the relation between the universal model of computation and the construction of an all-purpose machine.

Computing as a Mathematical Discipline

This chapter explores more closely the debates concerning correctness and illustrates the principles of formal verification for programsand the philosophical critiques to it. It finally closes the first part of this volume by formulating principles of formal computational validity.

Computing as an Experimental Discipline

This chapter considers directly the formal and epistemic properties characterizing computing as an experimental discipline and reconsiders an interpretation of validity and correctness.

Formal Relations

This chapter investigates further in formal detail the epistemic properties of the relations between computer simulations, models, and their target system. It reviews current analyses present in the relevant literature and advances a view on some formal methodological aspects required for a graded approach to such relations.

Computing as an Engineering Discipline

This Chapter reconsiders the engineering foundation of computing, overviews the related debate, and formulates a notion of physical computational validity.

The Laws of Evolution

This chapter explores the technologies that have made possible the rapid development of computingmachinery, essential for exploring the meaning of the laws of hardware and software evolution.

On the Nature of Algorithms

This chapter generalizes the notion of mechanical computation in the larger context of the notion of algorithm. While general recursion and its different interpretations are a product of mathematical research of the nineteenth and early twentieth centuries, much older is theideathatknowledge shouldbebasedonfiniteanddefiniteprocedures.Despite these ancient origins, the nature of algorithms and how their formal and conceptual definition should be given are still debated today.